Critical wall perturbations and a local free energy functional

On the basis of an ad hoc local free energy postulate recently advanced by de Gennes and Fisher, predictions are made for the local composition/magnetization perturbations induced near a wall by the presence of a second parallel wall at finite separation D, in a system at its bulk critical point. Despite some apparently serious limitations of the postulate, which are exposed, the most striking predictions for the behavior at large D are confirmed by new, exact calculations for the free energy of an n × ∞ spin $\text{1}\text{2}$ Ising model strip with distinct surface magnetic fields, H₁ and H_n, imposed on opposite boundaries.     

Frequency discrimination of complex tones; assessing the role of component resolvability and temporal fine structure

Thresholds for discriminating the fundamental frequency (FO) of a complex tone, FODLs, are small when low harmonics are present, but increase when the number of the lowest harmonic, N, is above eight. To assess whether the relatively small FODLs for N in the range 8-10 are based on (partly) resolved harmonics or on temporal fine structure information, FODLs were measured as a function of N for tones with three successive harmonics which were added either in cosine or alternating phase. The center frequency was 2000 Hz, and N was varied by changing the mean FO. A background noise was used to mask combination tones. The value of FO was roved across trials to force subjects to make within-trial comparisons. N was roved by +/- 1 for every stimulus, to prevent subjects from using excitation pattern cues. FODLs were not influenced by component phase for N= 6 or 7, but were smaller for cosine than for alternating phase once N exceeded 7, suggesting that temporal fine structure plays a role in this range. When the center frequency was increased to 5000 Hz, performance was much worse for low N, suggesting that phase locking is important for obtaining low FODLs with resolved harmonics.     

On shadowing: Ordinary and ergodic

The aim of this paper is to introduce the notion of ergodic shadowing for a continuous onto map which is equivalent to the map being topologically mixing and has the ordinary shadowing property. In particular, we deduce the chaotic behavior of a map with ergodic shadowing property. Moreover, we define some kind of specification property and investigate its relation to the ergodic shadowing property.     

On sparse estimation for semiparametric linear transformation models

Semiparametric linear transformation models have received much attention due to their high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002) [21] for linear transformation models to jointly estimate parametric and nonparametric terms. They showed that this procedure can yield a consistent and robust estimator. However, the problem of variable selection for linear transformation models has been less studied, partially because a convenient loss function is not readily available under this context. In this paper, we propose a simple yet powerful approach to achieve both sparse and consistent estimation for linear transformation models. The main idea is to derive a profiled score from the estimating equation of Chen et al. [21], construct a loss function based on the profile scored and its variance, and then minimize the loss subject to some shrinkage penalty. Under regularity conditions, we have shown that the resulting estimator is consistent for both model estimation and variable selection. Furthermore, the estimated parametric terms are asymptotically normal and can achieve a higher efficiency than that yielded from the estimation equations. For computation, we suggest a one-step approximation algorithm which can take advantage of the LARS and build the entire solution path efficiently. Performance of the new procedure is illustrated through numerous simulations and real examples including one microarray data.     

Searching and exploring properties of geometric configurations using dynamic software

The decline in enrolments and interest in advanced mathematics studies is of growing concern internationally. Previous research suggests that a range of factors can influence students' academic decisions. The focus of the paper is on one of these potential sources of influence— students' perceptions of the tertiary mathematics learning environment. Data from two large-scale surveys (N = 1883) and from a smaller number of interviews (N = 71) with students enrolled in tertiary mathematics courses at five Australian universities are presented and discussed. Collectively, the survey results and the interview data reveal considerable variations in the quality of the teaching and student support available in different mathematics departments. Students' comments were constructive and offered valuable ideas for improving the existing situation, retaining current students and attracting others to mathematics.     

A Modeling Perspective on Interpreting Rates of Change in Context

Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students’ abilities to describe and interpret rates of change in the context of exponential decay. In this article, we elaborate the characteristics of the model development sequence and we examine how students interpreted and described non-constant rates of change in context. We provide evidence for how a focus on the context made visible students’ reasoning about rates of change, including difficulties related to the use of language when describing changes in the negative direction. We argue that context and the use of language, forefronted in a modeling approach, should play an important role in supporting the development of students’ reasoning about changing phenomena.     

NMR Studies of Drugs. Applications of Achiral and Chiral Lanthanide Shift Reagents to a 5-Substituted-4-thiazolidinone

The 60 MHz ¹H NMR spectra of racemic 5-[[3,5-bis(1,1-dimethylethyl)-4-hydroxyphenyl]methyl]-4-thiazolidinone, 1, have been studied in CDCl₃ solution at 28° with the achiral lanthanide shift reagent (LSR), tris (6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium (III), 2, and the chiral LSRs, tris[3-(heptafluoropropylhydroxymethylene)- (+)-camphoratojeuropium(III), 3, and tris[3-(trifluoromethylhydroxymethylene-(+) -camphorato]europium (III), 4, Significant enantiomeric shift differences were observed in the presence of added 3, for the aryl protons of 1 that should permit direct determination of enantiomeric excess. Relative magnitudes of lanthanide-induced shift for the different nuclei of 1 with the three LSRs are compared and discussed in terms of preferred LSR binding sites. A favored conformation of 1 with respect to rotation about the C(5)-CH₂ bond is suggested.